The effects of a nonlinear energy sink during the instationary regime are analyzed by introducing uncertain parameters to verify the robustness of the transient spatial energy transfer when parameters are not well known. It was shown that it is possible to passively absorb energy from a linear nonconservative system (damped) structure to a nonlinear attachment weakly coupled to the linear one. This rapid and irreversible transfer of energy, named energy pumping, is studied by taking into account uncertainties on parameters, especially damping (since damping plays a great role and there is a lack of knowledge about it). In essence, the nonlinear subsystem acts as a passive nonlinear energy sink for impulsively applied external vibrational disturbances. The aim is to be able to apply energy pumping in practice where the nonlinear attachment realization will never perfectly reflect the design. Since strong nonlinearities are involved, polynomial chaos expansions are used to obtain information about random displacements. Not only are numerical investigations done, but nonlinear normal modes and the role of damping are also analytically studied, which confirms the numerical studies and shows the supplementary information obtained compared to a parametrical study.